Title: Development of a Multi-scale Mathematical Model for Chip-based Chromatography ABSTRACT The goal of this application is to develop a multi-scale mathematical model for chip-based Capillary Electrokinetic Chromatography (CEC) systems with applications to point-of-care technologies. Arising from the rapid growth of the number of samples to analyze and of their complexity on a lab-on-a-chip platform, effective and efficient chemical and biochemical separation becomes a pivotal element of lab-on-a-chip systems to achieve the goal of fast, high-throughput, reliable, and cost-effective operations promised by point-of-care technologies. CEC has both the efficiency of the Capillary Electrophoresis (CE) and the selectivity and sample capacity of the packed High Performance Liquid Chromatography (HPLC). CEC appears to be the simplest answer to realize fast and high-efficiency separation. However, one main issue that the driven flow is coupled to the properties of the column makes independent optimization of selectivity and flow generation impossible, preventing the widely industrial implementation of CEC. Therefore, a mathematical modeling tool capable of predicting the separation process, in advance, becomes critical to fully explore and exploit the potential of CEC systems. Nowadays, to understand the underlying physics, numerical simulation becomes one of the most important tools. It is particularly essential for CEC systems as the simultaneous optimization of both selectivity and flow field is challenging for experimental studies alone. But often direct numerical simulations are time- consuming, costly, and usually only applied for relatively short columns due to problem complexity. Thus to overcome the aforementioned shortcomings associated with direct numerical simulations, we propose to develop a multi-scale mathematical simulation tool to reduce the computational cost by many orders of magnitude. Numerical simulation is a key modern design tool as well. Computational studies can facilitate and speed up the design process by saving the time and cost to narrow down the optimal design solution via virtual prototyping of systems prior to fabrication of prototypes.